วีดีโอ

x=log48b8=1+log2b8+log3b8=1+1/3+log3b2/3=(4+log3b2)/3

Thanks sir ❤,🙏

Let y=2^x. Equation is y^3+y=(y^2)*(y+1)=130, or approximately, y^3=130. So estimate is y=5, which is the exact answer. So 2^x=5, so x=ln(5)/ln(2). Is the Math Olympiad this simple?

А что за буква v, в степени знаменателя?

Куча не нужных действий 12=4*3, 8 =4*2 Sqrt 12-sqrt 8=2*(sqrt 3-sqrt2) Далее 2*(sqrt 3 - sqrt2)*(sqrt3+sqrt2) Понятно что произведение двух скобок это разность квадратов и равно 1 Знаменатель 5+sqrt24=5+2sqrt6=3+2+2*sqrt 3*sqrt 2=(sqrt 3+sqrt 2)^2 Таким образом Sqrt (2/(sqrt 3+sqrt 2)^2)=sqrt 2/(sqrt 3+sqrt 2) Умножить на сопряженный множитель sqrt3 - sqrt2 Отсюда ответ Sqrt 6 - 2 Автор вообще не знает элементарных преобразовании, а решает в лоб. Не позорьтесь

Если 1/(sqrt 3+sqrt2) умножить на сопряженный множитель sqrt3 - sqrt2 то все просто получили ответ 2sqrt 3 и не надо ничего возводить в квадрат и делать кучу лишних действий

Solving this visually. First, find the square area first, which is side² You could see that the non-shaded area represent a quarter of a circle. But first, you need to get the area of the circle, which is π×r², in this case, the side is the radius. So it would be π×side² Simply divide by 4 to get the quarter, so its 1/4(π×side²) Now we got the quarter circle, to get the shaded area, subtract the square area with the quarter circle. So the answer is side² - 1/4(π×side²)

(side²)-(1/4x pi x r²)

X=log48/log8

125 + 5 = 130

this is so not a problem from any Maths Olympiad. the Olympiad make most people, including you and me, s**t in our pants.

А там в числителе 3^(х^какая-то галочка, даже не понятно что написано)

You are the real GOAT sir..❤❤

X^8 = 9^2 X = ±[9^(1/4)] X = ±[3^(1/2)] X = ±√3

2^27

You can solve it a bit easier by considering that 9^5 + 9^4 + 9^3 + 9^2 + 9= 10*9^4 + 10*9^2 + 9. This equals 65610 + 810 + 9.

1/3

(log base 8 (48) = x )crying in the corner

why didnt u do this instead: x/2 = x (multiply each side by 2) --> x = 2x (subtract x from each side) --> 0 = x (so x = 0)

3^2×3^5×3^3^3 =3^2×3^5×3^9 =3^16 3×3^4^4 =3×3^16=27 3^3 =3×3^3 =3

6÷2×3 can also be written as 6×3÷2. Whether you use left to right the answer is definitely 9. It is not 2×3 but ÷2×3=3/2. The question is not ambiguous. Excellent explanation, sir❤

Brilliant 👏

Какой логарифм, автор просто не знает что 8=2^3, 4=2^2 2^(2х)=2^3 2х=3 х=3/2 Три действия

delete this video🤣

ez

Why make it so complicated? You can simply rewrite 4^x as 2^2x , which gives: 2^2x + 2^2x = 16 Now, it's clear that you need two 8's (since 2^3=8) on the left side to match the 16 on the right side. Therefore, the only solution is x=1.5.

Sure you tried to prove a wrong answer will bull

Why not use log

This is another method which I believe is a bit simpler: Don’t subtract one until the end. I found 2^18 by thinking of it as 2^9 squared. I then found 512^2 by thinking of it as (500+12)(500+12). As (a+b)^2 = a^2+2ab+b^2, this is simply 500^2+(2)(500)(12)+12^2. 250000+12000+144. Finally subtract the 1.

Step 1: know the answer already. Very helpful.

After thinking for 10 seconds, I arrived at x = -2. Since x^2 gives 4 and x^3 gives -8. Then 4 - (-8) = 4 + 8 = 12